Q. The ends of two rods of different materials with their thermal conductivities, radii of cross-sections and lengths all are in the ratio 1:2 are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is $4\ cal/s$, that in the shorter rod in $cal/s$ will be
A) 1
B) 2
C) 8
D) 16
Explanation
(a) $\frac{dQ}{dt} = \frac{K\left( \pi r^{2} \right)d\theta}{dt} \Rightarrow \frac{\left( \frac{dQ}{dt} \right)_{s}}{\left( \frac{dQ}{dt} \right)_{l}} = \frac{K_{s} \times r_{s}^{2} \times l_{1}}{K_{l} \times r_{1}^{2} \times l_{s}} = \frac{1}{2} \times \frac{1}{4} \times \frac{2}{1}$
$\Rightarrow \left( \frac{dQ}{dt} \right)_{s} = \frac{\left( \frac{dQ}{dt} \right)_{l}}{4} = \frac{4}{4} = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.